H-infinity filtering with randomly occurring sensor saturations and missing measurements

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 ElsevierIn this paper, the H∞ filtering problem is investigated for a class of nonlinear systems with randomly occurring incomplete information. The considered incomplete information includes both the sensor saturations and the missing measurements. A new phenomenon of sensor saturation, namely, randomly occurring sensor saturation (ROSS), is put forward in order to better reflect the reality in a networked environment such as sensor networks. A novel sensor model is then established to account for both the ROSS and missing measurement in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. Based on this sensor model, a regional H∞ filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean-square asymptotically stable and the H∞-norm requirement is satisfied. Note that the regional l2 gain filtering feature is specifically developed for the random saturation nonlinearity. The characterization of the desired filter gains is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite program method. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61028008 and 60974030, the National 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany

On the application of a hybrid ellipsoidal-rectangular interval arithmetic algorithm to interval Kalman filtering for state estimation of uncertain systems

Modelling uncertainty is a key limitation to the applicability of the classical Kalman filter for state estimation of dynamic systems. For such systems with bounded modelling uncertainty, the interval Kalman filter (IKF) is a direct extension of the former to interval systems. However, its usage is not yet widespread owing to the over-conservatism of interval arithmetic bounds. In this paper, the IKF equations are adapted to use an ellipsoidal arithmetic that, in some cases, provides tighter bounds than direct, rectangular interval arithmetic. In order for the IKF to be useful, it must be able to provide reasonable enclosures under all circumstances. To this end, a hybrid ellipsoidal-rectangular enclosure algorithm is proposed, and its robustness is evidenced by its application to two characteristically different systems for which it provides stable estimate bounds, whereas the rectangular and ellipsoidal approaches fail to accomplish this in either one or the other case

A probabilistic interpretation of set-membership filtering: application to polynomial systems through polytopic bounding

Set-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic setting by employing sets of probability measures. Inference in set-membership estimation is thus carried out by computing expectations with respect to the updated set of probability measures P as in the probabilistic case. In particular, it is shown that inference can be performed by solving a particular semi-infinite linear programming problem, which is a special case of the truncated moment problem in which only the zero-th order moment is known (i.e., the support). By writing the dual of the above semi-infinite linear programming problem, it is shown that, if the nonlinearities in the measurement and process equations are polynomial and if the bounding sets for initial state, process and measurement noises are described by polynomial inequalities, then an approximation of this semi-infinite linear programming problem can efficiently be obtained by using the theory of sum-of-squares polynomial optimization. We then derive a smart greedy procedure to compute a polytopic outer-approximation of the true membership-set, by computing the minimum-volume polytope that outer-bounds the set that includes all the means computed with respect to P

Fault detection and isolation for linear dynamic systems

As modern control systems and engineering processes become increasingly more complex and integrated, the consequences of system failures and faults can be disastrous environmentally and economically. This thesis considers the fault detection and isolation (FDI) problem for linear time-invariant (LTI) systems subject to faults, disturbances and model uncertainties. Firstly, a novel on-line approach to the robust FDI problem for linear discrete-time systems is proposed by using input/output measurement analysis over a finite estimation horizon. Upper and lower bounds on the fault signal are computed at each sampling instant so that a fault is detected and isolated when its upper bound is smaller than zero or its lower bound is larger than zero. Moreover, a subsequent-state-estimation technique, together with an estimation horizon update procedure are given to allow the on-line FDI process to be repeated in a moving horizon scheme. Secondly, an optimal solution to theH−/H∞ fault detection (FD) problem is given for linear time-invariant systems subject to faults, disturbances and model uncertainties by using an observer-based approach. A new performance index is developed to capture both fault detection and disturbance rejection requirements which is particularly suitable for handling model uncertainties. A class of optimal solutions to the problem is then given in the form of simple linear matrix inequalities (LMI) with two degrees of freedom. By appropriately choosing these degrees of freedom, fault isolation can also be achieved. Thirdly, in order to improve the FD performance and remove restrictive rank assumptions, routinely made in the literature, observer-based FD problems are investigated at a single frequency and over a finite frequency range, respectively. An optimal solution is derived such that, at a given frequency, the static observer generates a residual signal which minimizes the sensitivity of the residual to disturbances while maintaining a minimum level of sensitivity to faults. Then, an initial investigation is carried out for the FD problem over a finite frequency range. A solution is derived in the form of an LMI optimization by using the generalized KYP lemma followed by a linearization procedure. Conditions under which this solution is optimal are also derived. Fully worked out numerical examples, mostly from the literature, are given to illustrate the effectiveness of all the proposed schemes

Decentralized Collision-Free Control of Multiple Robots in 2D and 3D Spaces

Decentralized control of robots has attracted huge research interests. However, some of the research used unrealistic assumptions without collision avoidance. This report focuses on the collision-free control for multiple robots in both complete coverage and search tasks in 2D and 3D areas which are arbitrary unknown. All algorithms are decentralized as robots have limited abilities and they are mathematically proved. The report starts with the grid selection in the two tasks. Grid patterns simplify the representation of the area and robots only need to move straightly between neighbor vertices. For the 100% complete 2D coverage, the equilateral triangular grid is proposed. For the complete coverage ignoring the boundary effect, the grid with the fewest vertices is calculated in every situation for both 2D and 3D areas. The second part is for the complete coverage in 2D and 3D areas. A decentralized collision-free algorithm with the above selected grid is presented driving robots to sections which are furthest from the reference point. The area can be static or expanding, and the algorithm is simulated in MATLAB. Thirdly, three grid-based decentralized random algorithms with collision avoidance are provided to search targets in 2D or 3D areas. The number of targets can be known or unknown. In the first algorithm, robots choose vacant neighbors randomly with priorities on unvisited ones while the second one adds the repulsive force to disperse robots if they are close. In the third algorithm, if surrounded by visited vertices, the robot will use the breadth-first search algorithm to go to one of the nearest unvisited vertices via the grid. The second search algorithm is verified on Pioneer 3-DX robots. The general way to generate the formula to estimate the search time is demonstrated. Algorithms are compared with five other algorithms in MATLAB to show their effectiveness

Assessment of human kinematic performance with non-contact measurements for tele-rehabilitation

 Aging of population is challenging the traditional rehabilitation services for various movement disorders. In the foreseeable future, tele-rehabilitation will be a contributive factor for the well-being of the older generation. This research has tackled a series of problems in developing an automated assessment tool for human kinematic performance in tele-rehabilitation with optoelectronic bio-kinematic motion capture devices and preliminarily confirmed its applicability

Interval Kalman Filtering Techniques for Unmanned Surface Vehicle Navigation

In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE does not endorse any of Plymouth University's products or services. Internal or personal use of this material is permitted. If interested in reprinting/republishing IEEE copyrighted material for advertising or promotional purposes or for creating new collective works for resale or redistribution, please go to http://www.ieee.org/publications_standards/publications/rights/rights_link.html to learn how to obtain a License from RightsLink.This thesis is about a robust filtering method known as the interval Kalman filter (IKF), an extension of the Kalman filter (KF) to the domain of interval mathematics. The key limitation of the KF is that it requires precise knowledge of the system dynamics and associated stochastic processes. In many cases however, system models are at best, only approximately known. To overcome this limitation, the idea is to describe the uncertain model coefficients in terms of bounded intervals, and operate the filter within the framework of interval arithmetic. In trying to do so, practical difficulties arise, such as the large overestimation of the resulting set estimates owing to the over conservatism of interval arithmetic. This thesis proposes and demonstrates a novel and effective way to limit such overestimation for the IKF, making it feasible and practical to implement. The theory developed is of general application, but is applied in this work to the heading estimation of the Springer unmanned surface vehicle, which up to now relied solely on the estimates from a traditional KF. However, the IKF itself simply provides the range of possible vehicle headings. In practice, the autonomous steering system requires a single, point-valued estimate of the heading. In order to address this requirement, an innovative approach based on the use of machine learning methods to select an adequate point-valued estimate has been developed. In doing so, the so called weighted IKF (wIKF) estimate provides a single heading estimate that is robust to bounded model uncertainty. In addition, in order to exploit low-cost sensor redundancy, a multi-sensor data fusion algorithm compatible with the wIKF estimates and which additionally provides sensor fault tolerance has been developed. All these techniques have been implemented on the Springer platform and verified experimentally in a series of full-scale trials, presented in the last chapter of the thesis. The outcomes demonstrate that the methods are both feasible and practicable, and that they are far more effective in providing accurate estimates of the vehicle’s heading than the conventional KF when there is uncertainty in the system model and/or sensor failure occurs.EPSR